New alternative statistic for testing several independent samples of correlation matrices in high dimension data

New alternative statistic for testing several independent samples of correlation matrices in high dimension data

Jennrich Jennrich statistic is one of the existing statistics which is used for testing the equality of several independent samples of correlation matrices. The statistic is gaining considerable importance in several areas of economics and financial markets. In these research areas, the number of v...

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Main Author: Atiany, Tareq A.M.
Format: Thesis
Language:eng
eng
eng
Published: 2018
Subjects:
QA273-280 Probabilities
Mathematical statistics
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https://etd.uum.edu.my/6889/2/s95832_01.pdf
https://etd.uum.edu.my/6889/3/s95832_02.pdf
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institution Universiti Utara Malaysia
collection UUM ETD
language eng
eng
eng
advisor Sharif, Shamshuritawati
topic QA273-280 Probabilities
Mathematical statistics
spellingShingle QA273-280 Probabilities
Mathematical statistics
Atiany, Tareq A.M.
New alternative statistic for testing several independent samples of correlation matrices in high dimension data
description Jennrich Jennrich statistic is one of the existing statistics which is used for testing the equality of several independent samples of correlation matrices. The statistic is gaining considerable importance in several areas of economics and financial markets. In these research areas, the number of variables, p, is usually larger than the sample size, n, which is known as high dimension data p > n. Subsequently, the estimation of correlation and covariance determinant will breakdown due to singularity problem. When this happens, Jennrich statistic is unable to function as the calculation involves the inversion of correlation matrix. Therefore, to resolve the aforementioned problem, this study develops an alternative statistic for testing several independent samples of correlation matrices in high dimension data. For this reason, the algebraic approach on the basis of vec operator, commutation matrix and Frobenius norm of upper-off-diagonal elements are used to derive the new asymptotic distribution for the new alternative statistic, namely * Z statistic. Simulation study was conducted by considering different number of variables, sample sizes, and correlation shifts to evaluate the performance of the new statistic. In addition, real data on Asia Pacific currencies structure during the Tohoku earthquake were applied to validate the new * Z statistic. The power of the * Z statistic is compared with the existing Jennrich statistic, and * T statistic through simulation study. As a result, the power of * Z statistic dominates the power of Jennrich statistic and * T statistic in all conditions, especially, when the shift in correlation matrix is at least 0.3 As a conclusion, the theoretical and simulation results are established and supported by desirable power of test. Meanwhile, investigation on real data indicates that the new alternative statistic can accommodate high dimension data.
format Thesis
qualification_name Ph.D.
qualification_level Doctorate
author Atiany, Tareq A.M.
author_facet Atiany, Tareq A.M.
author_sort Atiany, Tareq A.M.
title New alternative statistic for testing several independent samples of correlation matrices in high dimension data
title_short New alternative statistic for testing several independent samples of correlation matrices in high dimension data
title_full New alternative statistic for testing several independent samples of correlation matrices in high dimension data
title_fullStr New alternative statistic for testing several independent samples of correlation matrices in high dimension data
title_full_unstemmed New alternative statistic for testing several independent samples of correlation matrices in high dimension data
title_sort new alternative statistic for testing several independent samples of correlation matrices in high dimension data
granting_institution Universiti Utara Malaysia
granting_department Awang Had Salleh Graduate School of Arts & Sciences
publishDate 2018
url https://etd.uum.edu.my/6889/1/DepositPermission_s95832.pdf
https://etd.uum.edu.my/6889/2/s95832_01.pdf
https://etd.uum.edu.my/6889/3/s95832_02.pdf
_version_ 1747828123562409984
spelling my-uum-etd.68892021-08-09T04:38:44Z New alternative statistic for testing several independent samples of correlation matrices in high dimension data 2018 Atiany, Tareq A.M. Sharif, Shamshuritawati Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts and Sciences QA273-280 Probabilities. Mathematical statistics Jennrich Jennrich statistic is one of the existing statistics which is used for testing the equality of several independent samples of correlation matrices. The statistic is gaining considerable importance in several areas of economics and financial markets. In these research areas, the number of variables, p, is usually larger than the sample size, n, which is known as high dimension data p > n. Subsequently, the estimation of correlation and covariance determinant will breakdown due to singularity problem. When this happens, Jennrich statistic is unable to function as the calculation involves the inversion of correlation matrix. Therefore, to resolve the aforementioned problem, this study develops an alternative statistic for testing several independent samples of correlation matrices in high dimension data. For this reason, the algebraic approach on the basis of vec operator, commutation matrix and Frobenius norm of upper-off-diagonal elements are used to derive the new asymptotic distribution for the new alternative statistic, namely * Z statistic. Simulation study was conducted by considering different number of variables, sample sizes, and correlation shifts to evaluate the performance of the new statistic. In addition, real data on Asia Pacific currencies structure during the Tohoku earthquake were applied to validate the new * Z statistic. The power of the * Z statistic is compared with the existing Jennrich statistic, and * T statistic through simulation study. As a result, the power of * Z statistic dominates the power of Jennrich statistic and * T statistic in all conditions, especially, when the shift in correlation matrix is at least 0.3 As a conclusion, the theoretical and simulation results are established and supported by desirable power of test. Meanwhile, investigation on real data indicates that the new alternative statistic can accommodate high dimension data. 2018 Thesis https://etd.uum.edu.my/6889/ https://etd.uum.edu.my/6889/1/DepositPermission_s95832.pdf text eng public https://etd.uum.edu.my/6889/2/s95832_01.pdf text eng public https://etd.uum.edu.my/6889/3/s95832_02.pdf text eng public Ph.D. doctoral Universiti Utara Malaysia Aitkin, M., Nelson, W., & Reinfurt, K. H. (1968). Tests for correlation matrices. Biometrika, 327-334. Aktas, B. K. A. (2013). STATISTICAL POWER ANALYSIS. The 7th International Days of Statistics and Economics (pp. 578-587). Prague. Alfaro, J., & Ortega, J. F. (2009). 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